Algebraic expressions space combinations of variables , numbers, and at least one arithmetic operation.

for example, 2 x + 4 y − 9 is one algebraic expression.

** Term: ** each expression is consisted of of terms. A term deserve to be a signed number, a variable, or a consistent multiplied through a change or variables.

** Factor: ** Something i m sorry is multiply by other else. A element can it is in a number, variable, term, or a much longer expression. For example, the expression 7 x ( y + 3 ) has three factors: 7 , x , and ( y + 3 ) .

** Coefficient: ** The numerical element of a multiplication expression that includes a variable. Think about the expression in the number above, 2 x + 4 y − 9 . In the first term, 2 x , the coefficient is 2 : in the second term, 4 y , the coefficient is 4 .

** Constant: ** A number that cannot change its value. In the expression 2 x + 4 y − 9 , the ax 9 is a constant.

** choose Terms: ** Terms that contain the same variables such together 2 m , 6 m or 3 x y and 7 x y . If an expression has much more than one constant terms, those are likewise like terms.

Expression | word Phrases |

n + 5 | amount of a number and also 5 |

m − 7 | distinction of a number and also 7 |

6 x | Product the 6 and also a number |

y ÷ 9 | Quotient of a number and 9 |

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** Example: **

determine the terms, favor terms, coefficients, and constants in the expression.

9 m − 5 n + 2 + m − 7

First, we have the right to rewrite the subtractions together additions.

9 m − 5 n + 2 + m − 7 = 9 m + ( − 5 n ) + 2 + m + ( − 7 )

So, the ** terms ** room 9 m , ( − 5 n ) , m , 2 , and also ( − 7 ) .

** like terms ** are terms the contain the very same variables.

9 m and also 9 m are a pair of ** prefer terms ** . The consistent terms 2 and also − 7 are additionally like terms.

** Coefficients ** space the numerical components of a hatchet that has a variable.

So, here the ** coefficients ** space 9 , ( − 5 ) , and 1 . ( 1 is the coefficient of the term m .)

The ** consistent ** terms room the terms with no variables, in this instance 2 and also − 7 .

Algebraic expressions should be written and also interpreted carefully. The algebraic expression 5 ( x + 9 ) is ** not ** tantamount to the algebraic expression, 5 x + 9 .

watch the difference in between the two expressions in the table below.

native Phrases | Algebraic Expression |

five times the sum of a number and nine | 5 ( x + 9 ) |

Nine an ext than five times a number | 5 x + 9 |

In composing expressions because that unknown quantities, we regularly use conventional formulas. Because that example, the algebraic expression because that "the distance if the rate is 50 miles per hour and also the time is T hours" is D = 50 T (using the formula D = R T ).

an expression choose x n is referred to as a power. Below x is the base, and also n is the exponent. The exponent is the number of times the base is provided as a factor. The word expression for this expression is " x to the n th power."

here are few of the instances of making use of exponents.

native Phrases | Algebraic Expression |

7 times m come the 4th power | 7 m 4 |

The amount of x squared and also 12 times of y | x 2 + 12 y |

x cubed times y come the 6th power | See more: Convert 30 Kilos Is How Many Pounds And Ounces, 30 Kg To Lbs x 3 ⋅ y 6 |